# Leveraging Code Automorphisms for Improved Syndrome-Based Neural Decoding

arXiv: https://arxiv.org/abs/2605.03620 · HTML: https://mlsanity.com/paper/2605.03620/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 22 references that are in the map.
- First posted on arXiv 5 May 2026.

## Builds on (most cited first, 7 of 7)

- [Learning to Decode Linear Codes Using Deep Learning](https://mlsanity.com/paper/1607.04793/) (2016)
- [Error Correction Code Transformer](https://mlsanity.com/paper/2203.14966/) (2022)
- [Deep Learning for Decoding of Linear Codes - A Syndrome-Based Approach](https://mlsanity.com/paper/1802.04741/) (2018)
- [CrossMPT: Cross-attention Message-Passing Transformer for Error Correcting Codes](https://mlsanity.com/paper/2405.01033/) (2024)
- [Interplay Between Belief Propagation and Transformer: Differential-Attention Message Passing Transformer](https://mlsanity.com/paper/2509.15637/) (2025)
- [Hybrid Mamba-Transformer Decoder for Error-Correcting Codes](https://mlsanity.com/paper/2505.17834/) (2025)
- [On the Design and Performance of Machine Learning Based Error Correcting Decoders](https://mlsanity.com/paper/2410.15899/) (2024)

## Abstract (arXiv)

Syndrome-based neural decoding (SBND) has emerged as a promising deep learning approach for soft-decision decoding of high-rate, short-length codes. However, this approach still has substantial room for improvement. In this paper, we show how to leverage code automorphisms to enhance the ability of existing SBND models to learn and generalize through data augmentation during training and inference. As a result, for the short high-rate codes considered, we obtain models that closely approach MLD performance using small datasets and proper training. Our findings also suggest that many prior results for SBND models in the literature underestimate their true correction capability due to undertraining. Code to reproduce all results is available at: https://github.com/lebidan/sbnd.